Yes. The same thing happened to me two days ago - read-only and Time Machine could not backup. Could not find a way to change Read Only to Read & Write.
Did a bit of research and noted that OS Venture requires an APFS formatted Time Machine disk. Interesting as I'd upgraded to Venture just after it was released - a few weeks/months ago. But, Time Machine did not notice until two days ago that my Time Machine backup was formatted with the old Mac OS Extended format? In any event, used Disk Utility to check the backup disk and it passed multiple times. Disk Utility could also not reformat the disk. So, in frustration, deleted the backup disk in Time Machine preferences. Then, was able to reformat the disk to APFS and started a new Time Machine backup. Seems to work and as my backup is an older HD, not SSD, have changed backup timing to daily from hourly.
Seems I needlessly lost a few years of backups because of the change. Apple should address this problem & develop a needed fix so past backups can be saved when upgrading to Ventura...